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A137230
Composite numbers that are divisible by the number of their prime factors (counted with multiplicity).
3
4, 6, 10, 12, 14, 16, 18, 22, 24, 26, 27, 30, 34, 36, 38, 40, 42, 45, 46, 56, 58, 60, 62, 63, 66, 74, 75, 78, 80, 82, 84, 86, 88, 94, 96, 99, 100, 102, 104, 105, 106, 114, 117, 118, 120, 122, 132, 134, 136, 138, 140, 142, 144, 146, 147, 152, 153, 156, 158, 165, 166
OFFSET
1,1
COMMENTS
k is a term iff {k == 0 (mod BigOmega(k)) and k NOT prime}.
This sequence is obtained from A074946 by excluding all primes from that sequence.
LINKS
Eric Weisstein's World of Mathematics, Prime Factor.
EXAMPLE
k = 3; not a term because not a prime.
k = 4; a term because satisfies both k == 0 (mod bigomega(k)) and k NOT prime.
MATHEMATICA
Select[Range[200], CompositeQ[#] && Divisible[#, PrimeOmega[#]]&] (* Jean-François Alcover, Nov 11 2016 *)
PROG
(PARI) isok(c) = (c>1) && !isprime(c) && !(c % bigomega(c)); \\ Michel Marcus, Feb 28 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
William A. Tedeschi, Mar 07 2008
EXTENSIONS
Edited by Michel Marcus, Feb 28 2023
STATUS
approved